Skip to content
DraconiticResearch
Search Sources API
197,688 studies31 sourcesUpdated 47 min ago
PreprintarXiv licencearXiv

Existence and stability of capillary-gravity wave-borne vortices

  • Gregory Slease
  • Samuel Walsh
  • Runzhang Zhong
Open at sourcePDFDOICite

Abstract

In this paper, we consider the existence and stability of waves progressing through a finite-depth two-dimensional body of water that carry a vortex in their bulk. The waves are acted upon by gravity, and sit below a region of air at constant pressure, with the air--water interface being a free boundary along which capillary effects are incorporated. We consider two classes of vortices: point vortices, where formally the vorticity is a Dirac δ, and hollow vortices, where the vortex core is a region of constant pressure outside the fluid domain and about which there is a nonzero circulation. First, we prove that steady small-amplitude wave-borne point vortices exist for any subcritical Froude number and supercritical Bond number, and then show they are conditionally orbitally stable. Second, through a vortex desingularization argument, we construct capillary-gravity wave-borne hollow vortices. Notably, the wave speed is O(1) for both these families.

Related

  1. Global regularity for 2D gravity water waves with two retreating point vortices
    Lei Su, Qingtang Su, Siwei Wang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  2. Stabilization of gravity-capillary water waves with constant vorticity
    Qixing Ding, Jia-Cheng Zhao
    arXivPreprintarXiv licenceFull textAnalysis & PDEsOptimisation & controlarXiv
  3. Capillary-gravity water waves with compactly supported vorticity I: Local constructions and regular drift
    Lili Du, Changjun Zou
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  4. Isolated singularities of the capillary equation with negative gravity
    Bin Deng, Jiahuan Li, Yilu Liu +1
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. The stability of non-Abelian A4 vortices in SO(3) gauge theory
    Yoshihiko Abe, Tetsutaro Higaki, Kazuya Murakami +2
    arXivPreprintarXiv licenceFull textMathematical physicsHigh-energy & particle physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{slease2026existence,
  title = {{Existence and stability of capillary-gravity wave-borne vortices}},
  author = {Gregory Slease and Samuel Walsh and Runzhang Zhong},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.29791},
  eprint = {2609.29791},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.29791},
}
RIS
TY  - UNPB
TI  - Existence and stability of capillary-gravity wave-borne vortices
AU  - Gregory Slease
AU  - Samuel Walsh
AU  - Runzhang Zhong
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.29791
UR  - https://arxiv.org/abs/2609.29791
AB  - In this paper, we consider the existence and stability of waves progressing through a finite-depth two-dimensional body of water that carry a vortex in their bulk. The waves are acted upon by gravity, and sit below a region of air at constant pressure, with the air--water interface being a free boundary along which capillary effects are incorporated. We consider two classes of vortices: point vortices, where formally the vorticity is a Dirac δ, and hollow vortices, where the vortex core is a region of constant pressure outside the fluid domain and about which there is a nonzero circulation. First, we prove that steady small-amplitude wave-borne point vortices exist for any subcritical Froude number and supercritical Bond number, and then show they are conditionally orbitally stable. Second, through a vortex desingularization argument, we construct capillary-gravity wave-borne hollow vortices. Notably, the wave speed is O(1) for both these families.
ER  -